A pricing module is a computer program or a part of a computer program used to estimate future prices for one or more assets. Pricing modules use various economic or empirical financial models (a special class of which is known as pricing kernels) to generate price estimates. Inputs to pricing modules typically include economic variables such as interest rates, inflation, foreign exchange rates, etc. Outputs from the pricing modules are one or more estimated prices for assets priced at one or more future dates, as well as predictions for other economic variables. Thus, pricing modules are used to determine a projected future value of assets based on the economic factors used as inputs.
Many prior art pricing modules are based on models of the term structure of interest rates. Such models are typically based on the economic model disclosed in "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica 53, 363-384 (1985) and "A Theory of the Term Structure of Interest Rates," Econometrica 53, 385-408 (1985) both by J. C. Cox, J. E. Ingersoll and S. A. Ross. More recently, in "A Yield-Factor Model of Interest Rates," Mathematical Finance 6, 379-406 (1996) by D. Duffie and R. Kan, a class of affine term structure models where the yield of any zero-coupon bond is an affine function of the set of state variables was disclosed. The model disclosed by Duffie and Kan is an arbitrage-free model. Arbitrage is the simultaneous purchase and sale of the same, or similar, assets in two different markets for advantageously different prices. The absence of arbitrage in a pricing module is desirable because this prevents an investor from making "free money".
In a pricing module disclosed by Duffie and Kan, the affine model is fully characterized by a set of stochastic processes for state variables and a pricing kernel. The pricing kernel is a stochastic process that limits the prices on the assets and payoffs in such a way that no arbitrage is possible. However, these pricing modules and models on which they are based typically use state variables that are either particular asset yields or assumed and unobserved factors without a clear economic interpretation. Empirical applications of these affine models to interest rate data and foreign exchange data are well known in the art. See, for example, "An Affine Model of Currency Pricing," a working paper (1996) by D. Backus, S. Foresi and C. Telmer and "Specification Analysis of Affine Term Structure Models," a working paper (1997) by Q. Dai and K. K. Singleton.
Prior art pricing modules, however, have had little application beyond term structure modeling. Thus, a need exists for a pricing module that provides term structure modeling as well as equity modeling. More specifically, by using a term structure that varies stochastically over time in a partially predictable manner, models of the term structure may also be used for equity valuation. By applying a pricing module approach to both bonds and equities, the present invention provides a simple and unified arbitrage-free approach to pricing both fixed-income securities (e.g., bonds) and equity securities (e.g., stocks).